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Worksheet Grade 10 Engineering & Design

Marlin Cove Water Main: A Grade 10 Pipe Hydraulics Worksheet

A grade 10 worksheet sizing a fictional coastal water main: cross-sectional area, flow-to-velocity conversions, and the pressure a tank height delivers to the taps.

Objectives

  1. Students will calculate a water main's cross-sectional area and the velocity of water flowing through it.
  2. Students will convert a tank's height of water into pressure and check it against system pressure standards.

Vocabulary

Water main
A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: continuity, velocity, head, pressure

Teacher overview

A water main has to carry enough flow without moving the water too fast, and it has to deliver enough pressure at every tap, and both requirements can be checked with a few calculations. This worksheet has students size a new main for the fictional town of Marlin Cove, finding its cross-sectional area, the velocity of water inside it, and the pressure that the tank's height delivers to homes at different elevations. A common misconception in this math is that pressure depends on how much water is in the tank; it depends on the height of the water surface above the tap, so a home lower on the hill sees higher pressure than one near the tank, no matter how full the tank is.

Marlin Cove Water Main: A Grade 10 Pipe Hydraulics Worksheet — Grade 10 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Marlin Cove (a fictional town built for this worksheet) is installing a new water main with an inner diameter of 1.5 feet. The design flow in the main is 3,000 gpm. The water surface in the town's tank stands 140 feet above the main tap at the harbor. Systems usually run between 40 and 80 psi, and most states require at least 20 psi at every connection. Use Area = 0.785 × Diameter², the continuity equation Velocity = Flow ÷ Area, pressure (psi) = head (ft) × 0.433, and head (ft) = pressure (psi) × 2.31.

  1. Find the cross-sectional area of the 1.5-foot main in square feet, using Area = 0.785 × Diameter².

  2. Convert the design flow of 3,000 gpm to cubic feet per second, using the conversion that 1 cfs equals 448.8 gpm.

  3. Find the velocity of the water in the main in feet per second, dividing the flow in cfs (problem 2) by the area (problem 1).

  4. Convert the design flow of 3,000 gpm to million gallons per day, using the conversion that 1 MGD equals 694 gpm.

  5. Find the pressure at the harbor tap in psi, using the 140 feet of head above it and pressure = head × 0.433.

  6. Is the harbor-tap pressure from problem 5 inside the usual 40 to 80 psi operating range?

  7. A hillside neighborhood sits 70 feet above the harbor tap, so the water surface is 70 feet above it. Find the pressure at the hillside in psi.

  8. Does the hillside pressure from problem 7 meet the 20 psi minimum, and by about how much?

  9. A gauge at a fire hydrant reads 52 psi. How many feet of head does that pressure represent? Use head = pressure × 2.31.

  10. During peak demand the flow rises to 4,000 gpm in the same main. Find the new velocity in feet per second, first converting 4,000 gpm to cfs.

  11. Engineers try to keep main velocity at or below 5 feet per second to limit friction and water hammer. Does the 4,000 gpm case from problem 10 stay within that guideline?

  12. Explain why a larger-diameter main carries the same flow at a lower velocity than a smaller main.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: about 1.77 square feet.
    Area = 0.785 × 1.5² = 0.785 × 2.25 = 1.766, which rounds to about 1.77 square feet.

  2. Answer: about 6.68 cfs.
    3,000 gpm ÷ 448.8 gpm/cfs = 6.685, which rounds to about 6.68 cfs.

  3. Answer: about 3.78 feet per second.
    Velocity = 6.685 cfs ÷ 1.766 square feet = 3.785, which rounds to about 3.78 feet per second.

  4. Answer: about 4.32 MGD.
    3,000 gpm ÷ 694 gpm/MGD = 4.323, which rounds to about 4.32 MGD.

  5. Answer: about 60.6 psi.
    Pressure = 140 feet × 0.433 = 60.62, which rounds to about 60.6 psi.

  6. Answer: Yes.
    About 60.6 psi falls between 40 and 80 psi, so the harbor tap is inside the usual operating range.

  7. Answer: about 30.3 psi.
    The water surface is 70 feet above the hillside, so pressure = 70 × 0.433 = 30.31, which rounds to about 30.3 psi.

  8. Answer: Yes, by about 10 psi.
    30.3 psi is above the 20 psi minimum: 30.31 − 20 = 10.31, so the hillside clears the minimum by about 10 psi.

  9. Answer: about 120 feet.
    Head = 52 psi × 2.31 = 120.12, which rounds to about 120 feet.

  10. Answer: about 5.05 feet per second.
    4,000 gpm ÷ 448.8 = 8.913 cfs; velocity = 8.913 ÷ 1.766 = 5.046, which rounds to about 5.05 feet per second.

  11. Answer: No.
    About 5.05 feet per second is just above the 5-feet-per-second guideline, so the peak-demand case slightly exceeds it.

  12. Answer: A larger diameter means a larger area.
    Accept any answer explaining that velocity equals flow divided by area, so a larger cross-sectional area carries the same flow more slowly. Widening the pipe raises the area, which lowers the velocity for the same number of gallons per minute.

Differentiation

Support (below grade level)

Provide the four relationships (area, continuity, and the two pressure conversions) on a reference card with the constants filled in, and work problem 1 together so students find the area before they use it in the velocity step.

Extension (above grade level)

Ask students to suppose the same main carries the 4,000 gpm peak flow, then find the smallest inner diameter, in feet, that would keep the velocity at or below 5 feet per second, and to explain how that larger main would change the pressure delivered to the harbor tap.

ELL supports

Provide a labeled cross-section of the main and a side view of the tank and hillside, marking area, velocity, head, and pressure beside a short definition. Allow students to show problems 1 through 10 as numbered calculations and to answer problem 12 with a labeled sketch plus one sentence.